Question

1.7. Problem. (Sections 2.2-2.4)

(a) A quiz requires the student to match 10 terms with their correct definitions, where 10 definitions are given. If a student is just guessing, find the probability that they match at least 7 terms with their correct definitions.

(b) A quiz requires the student to match 10 terms with their correct definitions, where 11 definitions are given and one of the definitions does not match any of the terms. If a student is just guessing, find the probability that they match at least 7 terms with their correct definitions.

(c) A quiz requires the student to match 10 terms with their correct definitions, where 12 definitions are given and two of the definitions do not match any of the terms. If a student is just guessing, find the probability that they match at least 7 terms with their correct definitions.

Answer 1

(a) A quiz requires the student to match 10 terms with their correct definitions, where 10 definitions are given. If a student is just guessing, find the probability that they match at least 7 terms with their correct definitions.

Probability of success, p = 1/10 = 0.1

n = 10

X	P(X)
0	0.34868
1	0.38742
2	0.19371
3	0.05740
4	0.01116
5	0.00149
6	0.00014
7	0.00001
8	0.00000
9	0.00000
10	0.00000

Required probability = 0.00001 + 0.00000 + 0.00000 + 0.00000 = 0.00001

(b) A quiz requires the student to match 10 terms with their correct definitions, where 11 definitions are given and one of the definitions does not match any of the terms. If a student is just guessing, find the probability that they match at least 7 terms with their correct definitions.

Probability of success, p = 1/11 = 0.090909

n = 10

X	P(X)
0	0.38554
1	0.38554
2	0.17349
3	0.04627
4	0.00810
5	0.00097
6	0.00008
7	0.00000
8	0.00000
9	0.00000
10	0.00000

Required probability = 0.00000 + 0.00000 + 0.00000 + 0.00000 = 0.00000

(c) A quiz requires the student to match 10 terms with their correct definitions, where 12 definitions are given and two of the definitions do not match any of the terms. If a student is just guessing, find the probability that they match at least 7 terms with their correct definitions.

Probability of success, p = 1/12 = 0.0833

n = 10

X	P(X)
0	0.41890
1	0.38082
2	0.15579
3	0.03777
4	0.00601
5	0.00066
6	0.00005
7	0.00000
8	0.00000
9	0.00000
10	0.00000

Required probability = 0.00000 + 0.00000 + 0.00000 + 0.00000 = 0.00000